Question 2 .......................................................... [35 marks] Suppose that demand for a depletable and non-recyclable resource (e.g.. oil) is stable over time. This depletable resource is scarce (Q is the xed stock) with a constant marginal extraction cost (C). Suppcse that there is a backstop technolog' in the form of fullr renewable resource (e.g., solar energy) that can replace this depletable resource, which operates at a constant marginal cost K > G. Let R. and P} denote the quantity attracted and the price of the depletable resource in period t, respectively, and r represents the discount rate. Explain your intuition for the following hypothetical scenarios. You may want to high- light (whenever applicable) the changes in: (1) the time of exhaustion (if it is Fully depleted), (2) the initial price, (3) the evolution of price over time, (4) the rate of ex traction, and (5) the shadow price. Use the relevant plots to illustrate your answer. (a) [5 marks] Write down the Hotelling rule for the price P. to show the two deter- minants of price: marginal extraction cost (MEG) and marginal user cost (MUC). Explain how the price, extraction, MEG, and MUC evolve over time. (b) [10 marks] Suppose that there have been advancents in the backstop technology for the renewable resource, so it now has a lower marginal cost. Describe how this would impact the rate of extraction, the evolution of prices, and the resource depletion (if at all). (e) [10 marks] Suppose that the public campaigns force the suppliers in the market to incorporate the environmental costs into the price. Describe how adding a constant environmental cost (E) would impact the rate of extraction, the evolution of prices, and the resource depletion (if at all) (d) [10 marks] Suppose that public awareness lead to a lower demand for the depletable resource at every price level. Dacribe how this mum impact the rate of extraction, the evolution of prices, and the resource depletion (if at all)